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# The velocity $$v$$ of a particle at time $$t$$ is given by $${v}={at}+\frac{{b}}{{t}+{c}}.$$ The dimensions of $${a}$$, $${b}$$, and $${c}$$ are respectively: 1. $${\left[{LT}^{-2}\right],[{L}],[{T}]}$$ 2. $${\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]}$$ 3. $${\left[{LT}^2\right],[{LT}] \text { and }[{L}]}$$ 4. $${[{L}],[{LT}], \text { and }\left[{T}^2\right]}$$

Subtopic:  Dimensions |
85%
From NCERT
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In a vernier calliper, $$N$$ divisions of vernier scale coincides with ($$N\text-1$$) divisions of the main scale (in which length of one division is 1 mm). The least count of the instrument should be:
1. $$N~\text{mm}$$
2. $$N\text-1~\text{mm}$$
3. $$\frac{1}{10N}~\text{cm}$$
4. $$\frac{1}{N\text-1}~\text{mm}$$

Subtopic:  Measurement & Measuring Devices |
68%
From NCERT
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In certain vernier callipers, 25 divisions on the vernier scale have the same length as 24 divisions on the main scale. One division on the main scale is 1 mm long. The least count of the instrument is:

 1 0.04 mm 2 0.01 mm 3 0.02 mm 4 0.08 mm
Subtopic:  Measurement & Measuring Devices |
75%
From NCERT
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Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown?
It is given that the circular head translates $$\mathrm{P}$$ MSD in $$\mathrm{N}$$ rotations. ($$1$$ MSD $$=$$ $$\mathrm{1~mm}$$.)

1. $$\left(\frac{\mathrm{P}}{\mathrm{N}}\right)\left(2+\frac{45}{100}\right) \mathrm{mm}$$
2. $$\left(\frac{\mathrm{N}}{\mathrm{P}}\right)\left(2+\frac{45}{\mathrm{~N}}\right) \mathrm{mm}$$
3. $$\mathrm{P}\left(\frac{2}{\mathrm{~N}}+\frac{45}{100}\right) \mathrm{mm}$$
4. $$\left(2+\frac{45}{100} \times \frac{\mathrm{P}}{\mathrm{N}}\right) \mathrm{mm}$$

Subtopic:  Measurement & Measuring Devices |
51%
From NCERT
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A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are inserted together in series then the state is shown by the diagram (II). What is the zero error of the instrument? $$1~\text{msd}= 100~\text{csd}=1~\text{mm}$$

 1 $$-0.16~\text{mm}$$ 2 $$+0.16~\text{mm}$$ 3 $$+0.14~\text{mm}$$ 4 $$-0.14~\text{mm}$$
Subtopic:  Measurement & Measuring Devices |
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The main scale reading is $$-1$$ mm when there is no object between the jaws. In the vernier calipers, $$9$$ main scale division matches with $$10$$ vernier scale divisions. Assume the edge of the Vernier scale as the '0' of the vernier. The thickness of the object using the defected vernier calipers will be:

1. $$12.2~\text{mm}$$
2. $$1.22~\text{mm}$$
3. $$12.3~\text{mm}$$
4. $$12.4~\text{mm}$$

Subtopic:  Measurement & Measuring Devices |
62%
From NCERT
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In the vernier callipers given below, 9 main scale divisions matched with 10 vernier scale divisions. Assume the edge of the vernier scale as the '0' for the vernier scale. The thickness of the object using the defective vernier callipers will be:

1. 13.3 mm

2. 13.4 mm

3. 13.5 mm

4. 13.6 mm

Subtopic:  Measurement & Measuring Devices |
50%
From NCERT
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Planck's constant ($$h$$), speed of light in the vacuum ($$c$$), and Newton's gravitational constant ($$G$$) are the three fundamental constants. Which of the following combinations of these has the dimension of length?

 1 $$\frac{\sqrt{hG}}{c^{3/2}}$$ 2 $$\frac{\sqrt{hG}}{c^{5/2}}$$ 3 $$\frac{\sqrt{hG}}{G}$$ 4 $$\frac{\sqrt{Gc}}{h^{3/2}}$$
Subtopic:  Dimensions |
70%
From NCERT
NEET - 2016
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A student measured the diameter of a small steel ball using a screw gauge of least count $$0.001$$ cm. The main scale reading is $$5$$ mm and zero of circular scale division coincides with $$25$$ divisions above the reference level. If the screw gauge has a zero error of $$-0.004$$ cm, the correct diameter of the ball is:
1. $$0.521$$ cm
2. $$0.525$$ cm
3. $$0.053$$ cm
4. $$0.529$$ cm

Subtopic:  Measurement & Measuring Devices |
64%
From NCERT
NEET - 2018
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If dimensions of critical velocity $${v_c}$$ of a liquid flowing through a tube are expressed as $$\eta^{x}\rho^yr^{z}$$, where $$\eta, \rho~\text{and}~r$$ are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of $${x},$$ $${y},$$ and $${z},$$ respectively, will be:
1. $$1,-1,-1$$
2. $$-1,-1,1$$
3. $$-1,-1,-1$$
4. $$1,1,1$$

Subtopic:  Dimensions |
68%
From NCERT
NEET - 2015
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